SOLUTION: I need step by step instructions on how to solve the following: x + 2y - 2z + 4w = 1 y + z - w = 4 2z + 2w = -12 3w = 6 (x,y,z,w) = ?

Algebra ->  Linear-equations -> SOLUTION: I need step by step instructions on how to solve the following: x + 2y - 2z + 4w = 1 y + z - w = 4 2z + 2w = -12 3w = 6 (x,y,z,w) = ?      Log On


   

Question 576405: I need step by step instructions on how to solve the following:
x + 2y - 2z + 4w = 1
y + z - w = 4
2z + 2w = -12
3w = 6
(x,y,z,w) = ?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3w = 6

w = 6/3

w = 2
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2z + 2w = -12

2z + 2(2) = -12

2z+4 = -12

2z = -12-4

2z = -16

z = -16/2

z = -8

-----------------------

y + z - w = 4

y + (-8) - 2 = 4

y - 10 = 4

y = 4 + 10

y = 14

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x + 2y - 2z + 4w = 1

x + 2(14) - 2(-8) + 4(2) = 1

x + 28 + 16 + 8 = 1

x + 52 = 1

x = 1-52

x = -51

So the solution is (-51, 14, -8, 2)